44 citations · 117 across the 31 of their papers we have counts for
11 papers · 1 filter
Randomized Neural Networks for Integro-Differential Equations with Application to Neutron Transport
Haoning Dang, Fei Wang, Yifan Chen +3
Integro-differential equations arise in a wide range of applications, including transport, kinetic theory, radiative transfer, and multiphysics modeling, where nonlocal integral op…
Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations
Huan Zhang, Yifan Chen, Eric Vanden-Eijnden +1
Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial different…
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs
Pau Batlle, Yifan Chen, Bamdad Hosseini +2
We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods. The primary assump…
Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes
Yifan Chen, Houman Owhadi, Florian Schäfer
In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, G…
Exponentially Convergent Multiscale Finite Element Method
Yifan Chen, Thomas Y. Hou, Yixuan Wang
We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale s…
Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations
Yifan Chen, Ethan N. Epperly, Joel A. Tropp +1
The randomly pivoted partial Cholesky algorithm (RPCholesky) computes a factorized rank-k approximation of an N x N positive-semidefinite (psd) matrix. RPCholesky requires only (k…
Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations
Yifan Chen, Thomas Y. Hou, Yixuan Wang
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the waven…
Solving and Learning Nonlinear PDEs with Gaussian Processes
Yifan Chen, Bamdad Hosseini, Houman Owhadi +1
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identificat…
Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data
Yifan Chen, Thomas Y. Hou
There is an intimate connection between numerical upscaling of multiscale PDEs and scattered data approximation of heterogeneous functions: the coarse variables selected for derivi…
Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions
Yifan Chen, Thomas Y. Hou, Yixuan Wang
In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main result…
The quadratic Wasserstein metric for earthquake location
Jing Chen, Yifan Chen, Hao Wu +1
In [Engquist et al., Commun. Math. Sci., 14(2016)], the Wasserstein metric was successfully introduced to the full waveform inversion. We apply this method to the earthquake locati…